Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/43

Click to flip

43 Cards in this Set

  • Front
  • Back
in terms of sine and cosine, tan = ______
sin
____
cos
In terms of sine and cosine, csc = _____
1
____
sin
In terms of sine and cosine, cot = _____
cos
____
sin
In terms of sine and cosine, sec = _____
1
____
cos
What are three pythagorean identities
sin2x+cos2x=1

tan2x+1=sec2x

1+cot2x=csc2x
cofunction identity for cos?
sin((pi/2)-u)=cos u
cofunction identity for cot?
tan((pi/2)-u)= cot u
cofunction identity for csc?
sec((pi/2)-u)=csc u
cofunction identity for sin?
cos((pi/2)-u)=sin u
cofunction identity for tan?
cot((pi/2)-u)= tan u
cofunciton identity for sec?
csc((pi/2)-u)=sec u
3 even-odd identities
sin(-x)=-sin x
cos(-x)=cos x
tan(-x)=-tan x
Addition and subtraction formulas for sine?
sin(s+t)=sin s cos t+cos s sin t
sin(s-t)=sin s cos t - cos s sin t
Addition and subtraction formulas for cosine?
cos(s+t)=cos s cos t - sin s sin t
cos(s-t)=cos s cos t + sin s sin t
Addition and subtraction formulas for tangent?
tan(s+t)= tan s + tan t
_____________
1-tan s tan t

tan (s-t)= tan s - tan t
_____________
1+tan s tan t
0 radians = ___ degrees
0
pi/6 radians = _____ degrees
30
pi/3 radians= ____ degrees
60
pi/2 radians= ____ degrees
90
pi/4 radians = ____ degrees
45
cos and sine for 0 radians
1,0
cos and sine for pi/6 radians
sq(3)/2, 1/2
cos and sine for pi/4 radians
sq(2)/2
cos and sine for pi/2 radians
0,-1
What is double angle formula for sine
sin 2x= 2 sin x cos x
What are 3 double angle formulas for cosine
cos 2x= cos^2x-sin^2x
=1-2sin^2x
=2cos^2x-1
what is double angle formula for tangent
tan2x= 2 tan x
_________
1-tan^2x
name the sine sum-to-product formula when there is addition
sin x + sin y= 2sin(x+y)/2 cos(x-y)/2
name sum-to-product formula for sine when subtraction is used
sin x-sin y= 2 cos(x+y)/2 sin(x-y)/2
name sum-to-product formula for cosine when addition is used
cos x+cos y=2cos(x+y)/2 cos(x-y)/2
name sum-to-product formula for cos when subtraction is needed
cos x-cos y= -2sin(x+y)/2 sin(x-y)/2
what is product to sum formula for (sin u)(cos v)
1/2[sin(u+v)+sin(u-v)]
what is product to sum formula for] (cos u)(sin v)
1/2[sin(u+v)-sin(u-v)]
what is product to sum formula for (cos u)(cos v)
1/2[cos(u+v)+cos(u-v)]
what is product to sum formula for (sin u)(sin v)
1/2[cos(u-v)-cos(u+v)]
2 formulas for lowering powers for sin
sin^2x=1-cos2x
_______
2

sin x=sq(1-cos^2x)
what is half angle formula for sin?
sin(u/2)=+-sq((1-cos u)/2)
what is half angle formula for cos
cos(u/2)=+-sq((1+cos u)/2)
what are two half angle formulas for tan
tan(u/2)=(1-cos u)/sin u

OR

sin u/(1+cos u)
how do you decide whether to use + or - in sin and cos half angle formulas
depends on which quad in which u/2 lies
what is double angle formula for sine?
sin 2x=(2sinx)(cosx)
what are three double angle formulas fo cosine
cos 2x= cos^2x-sin^2x

1-2sin^x

2cos^2x-1
What is double angle formula for tangent
tan 2x= 2 tan x
_______
1-tan^2x